5 ideas
10792 | The substitutional quantifier is not in competition with the standard interpretation [Kripke, by Marcus (Barcan)] |
Full Idea: Kripke proposes that the substitutional quantifier is not a replacement for, or in competition with, the standard interpretation. | |
From: report of Saul A. Kripke (A Problem about Substitutional Quantification? [1976]) by Ruth Barcan Marcus - Nominalism and Substitutional Quantifiers p.165 |
10245 | One geometry cannot be more true than another [Poincaré] |
Full Idea: One geometry cannot be more true than another; it can only be more convenient. | |
From: Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics | |
A reaction: This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate. |
17423 | The essence of natural numbers must reflect all the functions they perform [Sicha] |
Full Idea: What is really essential to being a natural number is what is common to the natural numbers in all the functions they perform. | |
From: Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 2) | |
A reaction: I could try using natural numbers as insults. 'You despicable seven!' 'How dare you!' I actually agree. The question about functions is always 'what is it about this thing that enables it to perform this function'. |
17425 | To know how many, you need a numerical quantifier, as well as equinumerosity [Sicha] |
Full Idea: A knowledge of 'how many' cannot be inferred from the equinumerosity of two collections; a numerical quantifier statement is needed. | |
From: Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 3) |
17424 | Counting puts an initial segment of a serial ordering 1-1 with some other entities [Sicha] |
Full Idea: Counting is the activity of putting an initial segment of a serially ordered string in 1-1 correspondence with some other collection of entities. | |
From: Jeffrey H. Sicha (Counting and the Natural Numbers [1968], 2) |